Numerical and optimization analysis of natural convection and entropy-generation in wavy triangular cavity with Casson fluid under magnetohydrodynamics and radiation

Abstract Enclosure design is essential for thermal engineering technology and applications, including electronics, heat transfer equipment, power reactors, cooling mechanisms, solar energy systems, and nuclear power plants. This study aims to analyze the numerical and Response Surface Methodology (RSM) optimization for natural convection and entropy generation in a wavy triangular cavity with Casson fluid under inclined magnetohydrodynamic and radiation influences. The finite element approach (FEM) is utilized to compute the numerical solution for the simulation framework, while RSM is applied to determine the optimal heat transfer rate among four different parameters. The study presents streamlines, velocity profiles, isothermal lines, total entropy generation, and average Nusselt number in graphically and tabularly. The results show that an increase in the number of undulations and the Casson parameter leads to an increase in the thermal transfer rate and total entropy generation, whereas the Hartmann number has a decreasing effect on both. The Nusselt number rises with the rising number of undulations and the radiation parameter. The peak stream function is observed at an inclination angle of 60°. The significant R 2 value of 0.9967 shows a good agreement between the expected and actual values.